A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.

Explain how to find the arc length exactly, and then approximate it to one decimal place.

Part 1) The exact value of the arc length is / frac{25}{6}/pi / in

Part 2) The approximate value of the arc length is 13.1 / in

Step-by-step explanation:

ind the circumference of the circle

The circumference of a circle is equal to

C=2/pi r

we have

r=5 / in

substitute

C=2/pi (5)

C=10/pi / in

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

/frac{10/pi}{360} = / frac{x}{150}/ / / /x=10/pi * 150/360/ / / /x=/frac{25}{6}/pi / in

Find the approximate value of the arc length

To find the approximate value, assume

/pi = 3.14

substitute

/frac{25}{6} (3.14) = 13.1 / in